Null-plane formulation of Bethe-Salpeter qqq dynamics: Baryon mass spectra.

Abstract

The Bethe-Salpeter (BS) equation for a qqq system is formulated in the null-plane approximation (NPA) for the BS wave function, as a direct generalization of a corresponding QCD-motivated formalism developed earlier for qq\ifmmode\bar\else\textasciimacron\fi{} systems. The confinement kernel is assumed vector type (${\ensuremath{\gamma}}_{\ensuremath{\mu}}^{(1)}$${\ensuremath{\gamma}}_{\ensuremath{\mu}}^{(2)}$) for both qq\ifmmode\bar\else\textasciimacron\fi{} and qq pairs, with identical harmonic structures, and with the spring constant proportional, among other things, to the running coupling constant ${\ensuremath{\alpha}}_{s}$ (for an explicit QCD motivation). The harmonic kernel is given a suitable Lorentz-invariant definition [not ${\ensuremath{\square}}^{2}$${\ensuremath{\delta}}^{4}$(q)] , which is amenable to NPA reduction in a covariant form. The reduced qqq equation in NPA is solved algebraically in a six-dimensional harmonic-oscillator (HO) basis, using the techniques of SO(2,1) algebra interlinked with ${S}_{3}$ symmetry. The results on the nonstrange baryon mass spectra agree well with the data all the way up to N=6, thus confirming the asymptotic prediction M\ensuremath{\sim}${N}^{2/3}$ characteristic of vector confinement in HO form. There are no extra parameters beyond the three basic constants (${\ensuremath{\omega}}_{0}$,${C}_{0}$,${m}_{\mathrm{ud}}$) which were earlier found to provide excellent fits to meson spectra (qq\ifmmode\bar\else\textasciimacron\fi{}).